The present invention relates to the fields of image sensing and microscopy, and more specifically to methods, systems, and apparatuses for measuring the spatial frequency spectrum of an object using dynamic interference patterns.
Wide-field lens-based imaging systems form images by causing light diffracted or emitted by the object to interfere on a resolving detector or multi-element detector array. From the perspective of Fourier optics, the object may be considered as a coherent sum of sinusoidal Fourier components, such that the angle of light diffracted or emitted by each Fourier component varies with may be proportional to its spatial frequency. Because the optical system can collect only a cone of light defined by its numerical aperture (NA), off-axis light that carries high spatial frequency information may be rejected, thereby limiting spatial resolution. Wavefront aberrations in the optical path may further reduce resolution. Moreover, because the depth of field (DOF) of lens-based imaging systems typically has an inverse quadratic dependence on the NA, high-resolution imaging systems can maintain focus within a very limited depth range, typically only a few wavelengths. Furthermore, due to the challenges of manufacturing large, high NA, high-precision optics, the objective lens is typically be located within a working distance (WD) of only a few millimeters from the object in high-resolution microscopes.
Super-resolution wide-field microscopy techniques in the literature often exploit structured illumination in conjunction with a lens-based imaging system in order to surpass the diffraction resolution limit. Such techniques typically process a sequence of images acquired as the object is illuminated with multiple patterns, such as phase-shifted sinusoids, thereby effectively down-converting high-frequency Fourier components to lower spatial frequencies via the Moire effect. This approach is generally be subject to the same NA-dependent limit on DOF and WD as conventional imaging systems and trades imaging speed for gain in resolution.
Extending the lateral resolution limit even further, U.S. Pat. No. 6,255,642, incorporated herein by reference, may describe the use of an evanescent field produced by standing wave illumination due to total internal reflection at an interface with a transparent optical material in order to perform super-resolution imaging in the near-field. U.S. Pat. Nos. 5,394,268 and 6,055,097, incorporated herein by reference, may describe related structured illumination imaging techniques wherein the object is illuminated with interference patterns directed along the optical axis to reduce the effective DOF of the system, which may enable sub-wavelength axial sectioning.
On the other hand, lensless projection and diffraction tomography techniques may be used for high-resolution imaging of two-dimensional and three-dimensional structures by directly measuring the angular distribution of radiation transmitted or diffracted by an object, and are often used in wavelength regimes, such as X-rays, where lens-based optical imaging is challenging. These techniques typically rely on multiple radiation sources and detectors to measure Fourier components of the object along distinct paths in Fourier space, and a number of methods have been developed for reconstructing two- and three-dimensional images from such tomographic measurements, including the widely-used Filtered Backprojection algorithm.
A structured illumination remote sensing approach, called Fourier Telescopy, has been proposed (see Ustinov, N. D. et al., Sov. J. Quantum Electron. 17, 108-110 (1987), incorporated herein by reference) wherein the object is illuminated with one or more sinusoidal interference patterns that may be generated by an array of radiation sources and the response from the object is recorded with a single-element non-resolving detector to measure one or more Fourier components of a remote object.
U.S. Pat. No. 4,584,484, incorporated herein by reference, may describe a technique wherein an object is illuminated with a moving interference pattern produced by a pair of laser beams. In this technique, light transmitted by the object in response to the illumination is recorded as the angular separation or wavelength of the illuminating beams is mechanically scanned using an arrangement of mirrors during the motion of the pattern, thereby measuring the object's complex spatial Fourier transform along a direction. Additional “Fourier slices” may be acquired by rotating the illumination with respect to the object. An image may be synthesized by Fourier-transforming the acquired data.
U.S. Pat. Nos. 5,384,573 and 5,751,243, incorporated herein by reference, may describe an optical imager similar in principle to Synthetic Aperture Radar, where coherently scattered radiation from the object is detected as the optical plane orientation and the angular separation between an illumination beam and the line of sight of a single-element detector are varied. An optical heterodyne Fourier processor may be used to sequentially synthesize the image.
There is thus a need for tools and techniques that may not be limited to sequential sampling of Fourier components along a direction. Furthermore, there is a need for tools and techniques that may not rely on interference of discrete beams of radiation. Moreover, there is a need for tools and techniques that may provide a flexible, programmable means for measuring a variety of distributions of Fourier components in two and three-dimensional Fourier space through real-time electronic control. In addition, there is a need for tools and techniques that may provide for high speed one, two, and/or three dimensional image acquisition and synthesis.